There are various common (often Latin) phrases for various logic fallacies, such as post hoc ergo propter hoc, argumentum ad populum, slippery slope fallacy, etc. Is there a common phrase used to describe the fallacy of saying that because a claim seems so unusual or specific, it must be true, because 'nobody would ever make something that unusual up'?

First, reductio ad absurdum is not a fallacy - it is a proper argument "in which a proposition is disproven by following its implications logically to an absurd consequence." Then, Argumentum ad populum is a fallacy, but slippery slope fallacy has a counterpart - slippery slope argument which may or may not be a fallacy. I think your question would get better answers if you remove the wrong and ambiguous examples and provide a better definition than 'so absurd it must be true', which I can not properly distinguish from definition of an oxymoron.
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UnreasonMay 30 '11 at 10:00

Also, the truthfulness of a proposition does not imply a fallacy ("incorrect reasoning in argumentation resulting in a misconception")
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UnreasonMay 30 '11 at 10:08

@RiMMER, actually after thinking more about what is it that OP might be talking about a word popped up: he is talking about taking some proposition as true (axiom) - and though I don't believe that the absurdity, even in an absurd (or seemingly absurd) axioms can increase their believability, there is another word related to yours: dogmatic, which can be attributed to some of the fallacies (iep.utm.edu/fallacy)
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UnreasonMay 30 '11 at 10:25

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The ol' "You can't make this stuff up" logic fallacy? Do you really know people who use this in arguments to prove themselves correct?
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NeilMay 30 '11 at 11:57

6 Answers
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The biggest problem in finding a technical fallacy is that "absurd", in this context, isn't detailed enough. Why is it absurd? The idea that any absurd thing could be believed if it was simply absurd enough is not really true.

The idea of arguing something as true because no one would make it up is close to these fallacies:

a lie so "colossal" that no one would believe that someone "could have the impudence to distort the truth so infamously."

If you notice the quotes in that quote, you may wonder who coined the term. It was Adolf Hilter in his book Mein Kampf. In a certain sense, this Big Lie is an appeal to authority mixed with a strong pull on assumed morality.

Many tend to think of an appeal to authority as the style of bringing in a football player to advertise footballs: Since the player uses football, surely he knows which are best. But appeal to authority also includes what we are talking about here. Trying to list the steps it would look something like this:

Idea

Idea appears absurd

The person claiming Idea couldn't/wouldn't lie/imagine such an absurd thing

Therefore it is not absurd

Therefore Idea is plausible/true

The 3-4 step is the appeal to authority. Using English, these are all appeals to authority:

Well, they couldn't possibly make something like that up

All of humanity isn't clever enough to think of something like that

Sam is a terrible liar; therefore this isn't a lie

In conclusion, most "so absurd it must be true" arguments are likely to include one of these somewhere. They probably have other problems, too, considering how absurd they are. The specific term Big Lie is appropriate for someone who actually created such an absurd argument and is using it against the people who consider it too absurd to doubt.

This fallacy occurs when someone declares that any statement which appears too novel, too wonderful or astounding, must be false, simply because of the sensation of wonder or amazement the statement causes. There is nothing wrong with this sense of wonder causing us to take pause, and express doubt, but to rely solely on this sensation as a rebuttal is a logical fallacy. As Carl Sagan stated in Candle In The Dark, science (i.e. rational thinking) is a blend of wonder and skepticism, neither alone is sufficient

Isn't that the opposite of what I describe, though?
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JeddMay 30 '11 at 11:13

@Jedd, can you give a single example of what you are after, to illustrate the subject? I still maintain that I can not imagine a rhetorical figure that increases the absurdity of a proposition that at the same time increases the believability of the proposition.
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UnreasonMay 30 '11 at 11:19

"Appeal to Incredulity" is when the conclusions are too wonderful, therefore the arguments are fallacious.
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ThursagenMay 30 '11 at 11:19

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@Unreason well religion is the obvious one. If Jesus had only done mundane stuff like taught about love and forgiveness, would he have the same legendary status? It surely relies on the miracle claims to raise itself above that.
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JeddMay 30 '11 at 11:22

@Jedd, most of the logical fallacies were explained with religion, i.e. NO one has proved that God exists, therefore God doesn't exist. Why do people use religion as a comparison so much?
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ThursagenMay 30 '11 at 11:28

It does not fit all the attributes that you have prescribed, however it describes how one could come to accept propositions that are or seem to be unbelievable, incredible or fantastic.

On the other hand, I don't believe that credibility of such statements grows intrinsically from their unusualness. I think that your criteria: "it must be true since no one would make this up." is an afterthought, a reasoning (and yes, that is fallacious).

The original statement is not fallacious by itself - for example, such statement could have been: "It rained frogs". By itself it does not make me believe that it is true just because it sounds highly unlikely (or impossible); on the contrary, without any context I am more inclined to reject the statement as false. Still, it is a statement - either true or false. It contains no intrinsic fallacy and we can accept it either as assumption (used in consequent reasoning) or axiom (postulate) or as dogma.

It is fallacious to defend its truth value by saying "it must be true since no one would invent such a thing".

If you tell a lie big enough and keep repeating it, people will eventually come to believe it. The lie can be maintained only for such time as the State can shield the people from the political, economic and/or military consequences of the lie. It thus becomes vitally important for the State to use all of its powers to repress dissent, for the truth is the mortal enemy of the lie, and thus by extension, the truth is the greatest enemy of the State.

More of a rant then a phrase but I'm sure it's meaning qualifies as common English knowledge today as a result of the notoriety of the statement.